Can you claim a child for 6 months? He graduated and started working right after graduation in june?

[xmasbaby0]

If you claim a dependent you are claiming them for the whole year.   The year of graduation is tricky.  If they were younger than 24 and were a full-time student for 2023 until graduation, they can be claimed as a dependent.  That means on their own tax return they have to say that someone else can claim them.  

[JulieS]

No, you can't split the dependent. 

If he lived with you more than half of the year, and you provided more than half of his total support, you should claim him as dependent for the year, assuming he meets the other conditions.

Likewise if he was on his own, for more than half of the year and provided more than half of his own support, you should let him file independently.